This thesis presents a spectroscopic study of the 7F0 ---t5D0 transition of Eu3+ in EuC13 ·6H2 0, which is used to evaluate the potential performance of a quantum com puting system implemented in EuCla·6H2 0 and, more generally, in stoichiometric rare earth crystals. EuC13 ·6H2 0 has one of the narrowest optical inhomogeneous linewidths of any solid but this linewidth is shown to be still much larger than that required for practical quantum computing in a rare earth crystal. To assess the possibility of reducing the linwidth, the contributions of isotopic impurities to both the optical linewidth and line structure were investigated, and ligand isotopes were identified as a major source of both inhomogeneous broadening and structure on the optical transition, suggesting that the linewidth could be substantially reduced by isotopi cally purifying EuC13 ·6H20. The effect of ligand isotopes on the optical lifetime and coherence time was also investigated. It was found that fully deuterating the crystal to EuC13·6D20 substantially improves both the lifetime and coherence time. The satellite lines formed in the optical spectrum of a rare earth crystal when it is doped with another rare earth are proposed as qubits. A crucial step in char acterising EuCla ·6H20 for quantum computing is associating these satellite lines in EuC13 ·6H2 0 with crystallographic sites. A new method for associating sites with lines, which works for low symmetry crystals such as EuC13·6H20, is presented. This method involves modelling the splitting of the ground state hyperfine levels caused by the magnetic dipole-dipole interaction between a Kramers dopant and the Eu3+ ion. Using this method, most of the outer satellite lines in rare earth doped EuCla·6H2 0 were assigned to crystallographic sites. It has been proposed that the electronic interactions between these satellite lines be used to enact two-qubit gates in a rare earth quantum computer. These interac tions were measured between a number of different satellite lines using a new two laser spectral holeburning technique. Interactions of up to 46.081±0.005 MHz were observed, and this was the first time that electronic interactions between weakly coupled rare earth ions had been measured. The two most common interactions identified between rare earth ions in solids are electric dipole-dipole and exchange, but the observed interactions are stronger than expected from a electric dipole-dipole model and occur at too large a distance to be superexchange. It is shown that the development of a moderate-sized quantum processor, one with more than 10 qubits, in a stoichiometric rare earth crystal is feasible provided that the optical inhomogeneous linewidth is reduced below 1MHz. Demonstrations of three or four qubit devices should be possible using existing materials.
This thesis presents a spectroscopic study of the 7F0 ---t5D0 transition of Eu3+ in EuC13 ·6H2 0, which is used to evaluate the potential performance of a quantum com puting system implemented in EuCla·6H2 0 and, more generally, in stoichiometric rare earth crystals. EuC13 ·6H2 0 has one of the narrowest optical inhomogeneous linewidths of any solid but this linewidth is shown to be still much larger than that required for practical quantum computing in a rare earth crystal. To assess the possibility of reducing the linwidth, the contributions of isotopic impurities to both the optical linewidth and line structure were investigated, and ligand isotopes were identified as a major source of both inhomogeneous broadening and structure on the optical transition, suggesting that the linewidth could be substantially reduced by isotopi cally purifying EuC13 ·6H20. The effect of ligand isotopes on the optical lifetime and coherence time was also investigated. It was found that fully deuterating the crystal to EuC13·6D20 substantially improves both the lifetime and coherence time. The satellite lines formed in the optical spectrum of a rare earth crystal when it is doped with another rare earth are proposed as qubits. A crucial step in char acterising EuCla ·6H20 for quantum computing is associating these satellite lines in EuC13 ·6H2 0 with crystallographic sites. A new method for associating sites with lines, which works for low symmetry crystals such as EuC13·6H20, is presented. This method involves modelling the splitting of the ground state hyperfine levels caused by the magnetic dipole-dipole interaction between a Kramers dopant and the Eu3+ ion. Using this method, most of the outer satellite lines in rare earth doped EuCla·6H2 0 were assigned to crystallographic sites. It has been proposed that the electronic interactions between these satellite lines be used to enact two-qubit gates in a rare earth quantum computer. These interac tions were measured between a number of different satellite lines using a new two laser spectral holeburning technique. Interactions of up to 46.081±0.005 MHz were observed, and this was the first time that electronic interactions between weakly coupled rare earth ions had been measured. The two most common interactions identified between rare earth ions in solids are electric dipole-dipole and exchange, but the observed interactions are stronger than expected from a electric dipole-dipole model and occur at too large a distance to be superexchange. It is shown that the development of a moderate-sized quantum processor, one with more than 10 qubits, in a stoichiometric rare earth crystal is feasible provided that the optical inhomogeneous linewidth is reduced below 1MHz. Demonstrations of three or four qubit devices should be possible using existing materials.
We obtain a low optical inhomogeneous linewidth of 25 MHz in the stoichiometric rare-earth crystal EuCl_{3}·6H_{2}O by isotopically purifying the crystal in ^{35}Cl. With this linewidth, an important limit for stoichiometric rare-earth crystals is surpassed: the hyperfine structure of ^{153}Eu is spectrally resolved, allowing the whole population of ^{153}Eu^{3+} ions to be prepared in the same hyperfine state using hole-burning techniques. This material also has a very high optical density, and can have long coherence times when deuterated. This combination of properties offers new prospects for quantum information applications. We consider two of these: quantum memories and quantum many-body studies. We detail the improvements in the performance of current memory protocols possible in these high optical depth crystals, and describe how certain memory protocols, such as off-resonant Raman memories, can be implemented for the first time in a solid-state system. We explain how the strong excitation-induced interactions observed in this material resemble those seen in Rydberg systems, and describe how these interactions can lead to quantum many-body states that could be observed using standard optical spectroscopy techniques.
Rare-earth ions doped into a transparent crystal can have optically excited states with coherence times of milliseconds and hyperfine levels with coherence times of hours when cooled down to liquid helium temperatures. This makes them attractive for developing quantum computing hardware. A quantum transistor can be implemented in a rare-earth-ion-doped crystal by utilizing a dipole blockade effect, where one excited ion prevents nearby ions from being excited. By using single rare-earth ions as qubits, the quantum processor is believed to be scalable to several qubits. In this thesis a readout mechanism for qubits represented by single ions (Eu or Pr) in a Y2SiO5 crystal is explored. A single cerium ion, in the same crystal as the qubits, could potentially be used as an indicator ion for non-demolition quantum state detection of the qubits. Cerium has a strong transition with high fluorescence yield which makes it possible to detect single ions. A cerium ion can be controlled by a qubit via the dipole blockade effect, and fluoresce if the qubit is in state |1> but stay dark if the qubit is in state |0>. Relevant spectroscopic properties of Ce:Y2SiO5 are studied, as well as interactions between cerium ions and qubit ions. The inhomogeneous and homogeneous linewidth of the Ce:Y2SiO5 4f-5d transition is measured and fluorescence spectra for ions in site 1 and site 2 are characterized. The change in electric dipole moment as a cerium ion is brought to the excited state is measured. The static dipole interaction between a single cerium ion and a qubit ion is shown to be strong enough for efficient qubit readout. Energy transfer from cerium to qubit ions is investigated. A lower bound on the cerium-qubit distance is found in order to avoid energy transfer. Satellite lines belonging to cerium-qubit pairs are mapped out. A microscope set-up is built to detect single ions in a crystal. Single ion detection is believed to be within reach.
Abstract Doping erbium ions into europium-based hosts offers a promising platform for quantum repeater nodes, combining europium’s exceptional coherence properties for long-term quantum storage with erbium’s microwave compatibility and direct telecom-band emission for efficient optical interfacing. In this work, we investigated erbium-doped EuCl3 · 6H2O stoichiometric crystals as a candidate for such nodes. We demonstrate that erbium doping shifts the optical transition frequencies of nearby Eu3+ ions, producing well resolved satellite lines in the inhomogeneous absorption profile. We experimentally probe the coupling between Er3+ and Eu3+ ions under varying temperature and magnetic field conditions, quantifying the interaction strength, which ranges from tens to hundreds of kilohertz, depending on field orientation, magnitude, and the lattice position of the Eu3+ ions. At 60 mK and a moderate magnetic field of 0.1 T, we observed a strong frozen core effect from Er3+ spins, substantially extending the Eu3+ optical coherence time from 62 us to 162 us, approaching the lifetime limit, and enabling hour-long hyperfine state lifetimes. These results underscore the potential of dual-species rare-earth systems for photonic quantum technologies and highlight their promise for precise quantum control.
In this thesis, crystals of yttrium orthosilicate (Y2SiO5) that are randomly doped with another rare-earth element, such as praseodymium (Pr), europium (Eu), or cerium (Ce), are investigated with lasers locked to ultra-stable cavities using the Pound-Drever-Hall locking technique. Many of these rare-earth elements have long-lived 4f-4f transitions, hundreds of microseconds to a few milliseconds, with even longer ground hyperfine lifetimes of up to several days. The coherence properties are, to the best of the author's knowledge, the longest achieved for any material, currently with a record of six hours for the nuclear spin states of Eu3+:Y2SiO5 measured at cryogenic temperatures. Furthermore, due to natural trapping and differences in the local environments, each dopant ion experiences a slightly different crystal field, and thus an inhomogeneity in the 4f-4f transition exists between all ions in a crystal. Since the homogeneous linewidth is in the order of kHz or below, whereas the inhomogeneous profile can be several GHz wide, these materials have dense storing capabilities.This thesis explores how light interacts with such rare-earth-ion-doped crystals; how the absorption and light polarization varies during propagation; how spectral features in the inhomogeneous absorption profile can be tailored to create narrowband spectral filters; how the speed of light is slowed down significantly in such narrow transmission windows; and how that can be used to either frequency shift incoming light, control its group velocity, or temporally compress pulses. It also uses rare-earth-ions to research quantum computing, the field of using quantum mechanical effects such as superpositions and entanglements to outperform classical computers on certain specific problems. This is done by examining how two-color pulses can be used to rapidly induce coherence from an initially mixed state; how qubit-qubit interactions can be performed experimentally using ensemble qubits, which opens the door to two-qubit experiments such as the CNOT-gate and entanglements; how a scalable quantum computer might be constructed using a single ion qubit approach with a dedicated readout ion and buffer ion(s) to improve readout fidelity; and how cerium is investigated as a candidate for such a dedicated readout ion.
The main aim of this work, was to lay the foundations for the experimental realisation of a quantum mechanical controlled NOT gate in rare-earth-metal-ion-doped crystals. Small amounts of rare-earth elements, added during the growth of some inorganic crystals, will become substituted into the crystal lattice as trivalent ions. The trivalent rare-earth-metal ions between cerium, with atomic number 58, and ytterbium, with atomic number 70, have a partly filled 4f shell, which does not extend spatially outside the full 5s and 5p shells. The 4f vacancies make electronic inner shell transitions possible between spectroscopic 4f terms. Some of these optical transitions have coherence times of the order of milliseconds, when the crystals are cooled down to ~ 4 K. There are several reasons for these extraordinary coherence times, which are approximately 8 orders of magnitude greater than those typical for electronic transitions in solids. The most important one is the cage-like shield which the outer 5s and 5p shells provide for the 4f electrons. Furthermore, since these ions are naturally trapped inside the crystal lattice there is no Doppler broadening of the line-width. The coherence properties of these optical transitions is one of the features that makes these materials attractive for use as a solid-state platform for quantum computing, using these ions as qubits. Another appealing characteristic is the fact that different ions have different optical resonance frequencies, which means that ions belonging to different qubits, which only have nm separation, can still be addressed separately by using different laser frequencies. Since the inter-ion spacing is so small, it is possible to make two ions interact strongly, although they are well shielded, through a permanent dipole-dipole interaction. This interaction can be turned on and off by switching between two different ways of encoding the qubit, a most useful feature. When the qubit is represented as a superposition between two ground state hyperfine levels, the interaction is turned off. The interaction is turned on selectively by transferring this superposition to the optical transition with a pi-pulse, for the specific ions that are to interact. This thesis describes how peaks of ions, absorbing on a single transition, residing in spectral pits with no other ions, have been isolated. It is shown how these ions can be coherently transferred between hyperfine levels via the optically excited state, how the interaction between such peaks of ions representing qubits can be turned on and off, and how subgroups of ions with strong interaction can be distilled out. All the work described here has been performed using the ensemble approach. The ensemble approach will, however, be difficult to scale up to large numbers of qubits. A method employing a single ion in each qubit, using a specialised ion for readout, has therefore also been proposed. The rare-earth-metal-ion-based quantum computing experiments require a laser with coherence properties which at least match those of the material. To this end a frequency stabilisation system was developed for a dye laser. This system uses a transient spectral hole in a rare-earth-metal-ion-doped crystal, of the same kind that is used in the experiments, as frequency reference, and is to the authors knowledge the first demonstration of locking a dye laser to a spectral hole. This system provides a line-width of 1 kHz on a 10 microseconds timescale and a frequency drift below 1 kHz/s.
This thesis presents a spectroscopic study of Pr3+ ions in a novel passive waveguide architecture. To make this structure, the high refractive glass TeO2 was selected as the thin film and it was deposited on a Pr3+:Y2SiO5 crystal. In this waveguide, the 3H4 to 1D2 transition of Pr3+ ions were probed by the optical evanescent field extending into the substrate. The main concern in assessing the suitability of this material for quantum information applications was ensuring that the coherence properties of rare-earth ions, making them suitable for quantum information purposes, are preserved in this architecture. After which, to make low loss devices with these waveguides, efficient coupling techniques had to be developed. To prove that the coherence properties of the rare-earth ion doped crystal were preserved, the critical parameters of inhomogeneous linewidth, the absorption of the ions, the coherence time and spin lifetimes of the Pr3+ ions were studied. The inhomogeneous linewidth of evanescent coupled ions was about 10.0 GHz, which was consistent with the linewidth of bulk samples with the same Pr3+ doping concentration (Hedges, 2011). The absorption due to the evanescent coupling was 9.38 dB, approximately 90% of what was expected with respect to the bulk crystal with the same doping concentration. Therefore, despite using the evanescent field, the absorption is high enough for quantum memory applications. An optical coherence time of about 121 microseconds was measured, which corresponded to a homogeneous linewidth of about 2.6 kHz. This is very close to bulk sample measurements of 111 microseconds, with the same temperature and doping concentration (R. W. Equall, 1995). The spin state lifetime observed was about 9.8 s, which is also very close to the bulk sample measurement of 8.67 s (Mieth, 2016). Initial Stark shifting experiments were performed to determine whether the active ions in the substrate of the passive waveguides could be electrically controlled by applying a small voltage to electrodes on the thin film. In these experiments with a voltage change of 100 mV, the measured holewidth broadening was increasing about 0.55 MHz, which was similar to the calculated values of 0.45 MHz. The Stark coefficient for site 1 was 51.6 kHzcm/V along the D2 axis of the crystal (site 1 will be explained in Section 4.3). (F.R. Graf, 1997). Prism coupling and grating coupling were used to couple light to the ions in the substrate. Prism coupling is an easy and quick method to couple light into a waveguide and observe the properties of the system. However, grating coupling is much more practical when moving towards building a device using this method. The measurements described above indicated that the properties of ions interacting with the evanescent tail of the waveguide mode were consistent with those of bulk ions. This investigation also showed that depositing a glass thin film on a rare-earth ion doped crystal was not affecting the good coherence properties of the substrate. These results establish the foundation for large, integrated, controllable and high performance rare earth ion quantum waveguide systems.